1. A nonzero vector that, when multiplied by a square matrix, yields a scalar multiple of itself; used in linear algebra and applied mathematics.
Usage: technical; mathematics

Examples

• The eigenvector of a matrix remains in the same direction after the matrix transformation.
• In physics, eigenvectors represent the natural modes of vibration in a system.
• To find an eigenvector, you must first calculate the eigenvalues of the matrix.
• The principal eigenvector of a correlation matrix reveals the direction of maximum variance.
• Machine learning algorithms often use eigenvectors to reduce data dimensionality.
• Each eigenvector corresponds to a specific eigenvalue in the eigenvalue equation.